Como se usa 'disculparse' en contextos diferentes?

Question

If I want to say some of the following things, how would I use 'disculparse'? would it be appropriate for these contexts?

-allow me to apologize
-I am very sorry
-please accept my apology

In Portugues, I know that you can simply say 'disculpe' when you want to apologize, for example instead of lo siento. But in that language as well, I never got the hang of how to use disculpar in other ways. Thanks you for the help!

Answer 1

-allow me to apologize

Tengo que pedirte (pedirle) perdón.
Déjame disculparme. (Déjeme disculparme)

-I am very sorry

Lo siento mucho.

-please accept my apology

Te ruego me disculpes.
Le ruego me disculpe.

Answer 2

"Permita que me disculpe"
"Lo siento much".
"Favor que acepte usted mis disculpas."

Answer 3

-allow me to apologize: "Permítame que me disculpe/Permítame disculparme" "Déjeme disculparme"
-I am very sorry: "Lo siento mucho"
-please accept my apology: "Por favor, acepte mis disculpas"